谁给我50道一元二次方程,要求解出来的! 帮我找50道一元二次方程计算题和50道二次根式计算题(带答案...
\u8c01\u53ef\u4ee5\u7ed9\u6211\u627e50\u9053\u4e8c\u6b21\u6839\u5f0f\u548c50\u9053\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\uff08\u5e26\u7b54\u6848\u54e6\uff09\uff08\u6700\u597d\u5e26\u8fc7\u7a0b\uff09\u62dc\u6258\u4e86\u5404\u4f4d \u8c22\u8c221.X(2-\u221a2)=(\u221a2-2) X(2-\u221a2)=(\u221a2-2) X(2-\u221a2)=-1(2-\u221a2\uff09 x=1 2.(\u221a5\uff0b\u221a2)\uff0d(\u221a5\uff0d\u221a2) \uff1d(\u221a5\uff0b\u221a2\uff0b\u221a5\uff0d\u221a2)(\u221a5\uff0b\u221a2\uff0d\u221a5\uff0b\u221a2) \uff1d2\u221a5*2\u221a2 \uff1d4\u221a10 3.\u221a8\uff0b3\u221a(1/3)\uff0d1/(\u221a2)\uff0b(\u221a3)/2 \uff1d2\u221a2\uff0b3*(\u221a3)/3\uff0d(\u221a2)/2\uff0b(\u221a3)/2 \uff1d2\u221a2\uff0b\u221a3\uff0d(\u221a2)/2\uff0b(\u221a3)/2 \uff1d(3/2)\u221a3\uff0b(3/2)\u221a2 4.(\u221a3\uff0b\u221a2\uff0b\u221a5)(\u221a3\uff0d\u221a2\uff0d\u221a5) \uff1d(\u221a3\uff0b\u221a2\uff0b\u221a5)[\u221a3\uff0d(\u221a2\uff0b\u221a5)] \uff1d(\u221a3)\uff0d(\u221a2\uff0b\u221a5) \uff1d3\uff0d(2\uff0b5\uff0b2\u221a10) \uff1d3\uff0d7\uff0d2\u221a10 \uff1d\uff0d4\uff0d2\u221a10 5.\u221a8-2\u221a32+\u221a50 =5*3\u221a2-2*4\u221a2+5\u221a2 =\u221a2(15-8+5) =12\u221a2 6.\u221a6-\u221a3/2-\u221a2/3 =\u221a6-\u221a6/2-\u221a6/3 =\u221a6/6 7. (\u221a45+\u221a27)-(\u221a4/3+\u221a125) =(3\u221a5+3\u221a3)-(2\u221a3/3+5\u221a5) =-2\u221a5+7\u221a5/3 8.(\u221a4a-\u221a50b)-2(\u221ab/2+\u221a9a) =(2\u221aa-5\u221a2b)-2(\u221a2b/2+3\u221aa) =-4\u221aa-6\u221a2b 9.(\u221a32-3\u221a3)(4\u221a2+\u221a27) =(4\u221a2-3\u221a3)(4\u221a2+3\u221a3) =(4\u221a2)^2-(3\u221a3)^2 =32-27 =5 10.1+\u221a2-\u221a3\uff09\uff081-\u221a2+\u221a3\uff09 =[1+(\u221a2-\u221a3)][1-(\u221a2-\u221a3)] =1-(\u221a2-\u221a3)^2 =1-(2+3+2\u221a6) =-4-2\u221a6 \u62fc\u4f60\u5341\u9053\u3002\u3002\u6c42\u91c7\u7eb3\u3002 \u8ffd\u95ee\uff1a \u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b \u53ef\u5426\u5728\u7ed9\u51e0\u9053 \u56de\u7b54\uff1a 1\uff09x^2+4x+3-15=0 x^2+4x-12=0 (x-2)(x+6)=0 \u5219x=2\u6216 -6 \uff082) (2x-1)(x+3\uff09=0 \u5219x=1/2 \u6216 -3 (3) (x-\u221a2)^2=0 \u5219x=\u221a2 (4) 1/2(x^2+2x+1)+1/8-1/2=0 1/2(x+1)^2=3/8 (x+1)^2=3/4 \u5219x=\u221a3/2 -1 \u6216 -\u221a3/2 -1 \uff085\uff09 3\uff08x-2)^2+x(x-2\uff09=0 \uff08x-2)[3(x-2)+x]=0 (x-2\uff09\uff084x-6)=0 \u5219x=2 \u6216 3/2 \u8865\u5145\uff1a \u6c42\u91c7\u7eb3\u554a\u3002
1\uff09 66x+17y=3967 25x+y=1200 \u7b54\u6848\uff1ax=48 y=47 (2) 18x+23y=2303 74x-y=1998 \u7b54\u6848\uff1ax=27 y=79 (3) 44x+90y=7796 44x+y=3476 \u7b54\u6848\uff1ax=79 y=48 (4) 76x-66y=4082 30x-y=2940 \u7b54\u6848\uff1ax=98 y=51 (5) 67x+54y=8546 71x-y=5680 \u7b54\u6848\uff1ax=80 y=59 (6) 42x-95y=-1410 21x-y=1575 \u7b54\u6848\uff1ax=75 y=48 (7) 47x-40y=853 34x-y=2006 \u7b54\u6848\uff1ax=59 y=48 (8) 19x-32y=-1786 75x+y=4950 \u7b54\u6848\uff1ax=66 y=95 (9) 97x+24y=7202 58x-y=2900 \u7b54\u6848\uff1ax=50 y=98 (10) 42x+85y=6362 63x-y=1638 \u7b54\u6848\uff1ax=26 y=62 (11) 85x-92y=-2518 27x-y=486 \u7b54\u6848\uff1ax=18 y=44 (12) 79x+40y=2419 56x-y=1176 \u7b54\u6848\uff1ax=21 y=19 (13) 80x-87y=2156 22x-y=880 \u7b54\u6848\uff1ax=40 y=12 (14) 32x+62y=5134 57x+y=2850 \u7b54\u6848\uff1ax=50 y=57 (15) 83x-49y=82 59x+y=2183 \u7b54\u6848\uff1ax=37 y=61 (16) 91x+70y=5845 95x-y=4275 \u7b54\u6848\uff1ax=45 y=25 (17) 29x+44y=5281 88x-y=3608 \u7b54\u6848\uff1ax=41 y=93 (18) 25x-95y=-4355 40x-y=2000 \u7b54\u6848\uff1ax=50 y=59 (19) 54x+68y=3284 78x+y=1404 \u7b54\u6848\uff1ax=18 y=34 (20) 70x+13y=3520 52x+y=2132 \u7b54\u6848\uff1ax=41 y=50 (21) 48x-54y=-3186 24x+y=1080 \u7b54\u6848\uff1ax=45 y=99 (22) 36x+77y=7619 47x-y=799 \u7b54\u6848\uff1ax=17 y=91 (23) 13x-42y=-2717 31x-y=1333 \u7b54\u6848\uff1ax=43 y=78 (24) 28x+28y=3332 52x-y=4628 \u7b54\u6848\uff1ax=89 y=30 (25) 62x-98y=-2564 46x-y=2024 \u7b54\u6848\uff1ax=44 y=54 (26) 79x-76y=-4388 26x-y=832 \u7b54\u6848\uff1ax=32 y=91 (27) 63x-40y=-821 42x-y=546 \u7b54\u6848\uff1ax=13 y=41 (28) 69x-96y=-1209 42x+y=3822 \u7b54\u6848\uff1ax=91 y=78 (29) 85x+67y=7338 11x+y=308 \u7b54\u6848\uff1ax=28 y=74 (30) 78x+74y=12928 14x+y=1218 \u7b54\u6848\uff1ax=87 y=83 (31) 39x+42y=5331 59x-y=5841 \u7b54\u6848\uff1ax=99 y=35 (32) 29x+18y=1916 58x+y=2320 \u7b54\u6848\uff1ax=40 y=42 (33) 40x+31y=6043 45x-y=3555 \u7b54\u6848\uff1ax=79 y=93 (34) 47x+50y=8598 45x+y=3780 \u7b54\u6848\uff1ax=84 y=93 (35) 45x-30y=-1455 29x-y=725 \u7b54\u6848\uff1ax=25 y=86 (36) 11x-43y=-1361 47x+y=799 \u7b54\u6848\uff1ax=17 y=36 (37) 33x+59y=3254 94x+y=1034 \u7b54\u6848\uff1ax=11 y=49 (38) 89x-74y=-2735 68x+y=1020 \u7b54\u6848\uff1ax=15 y=55 (39) 94x+71y=7517 78x+y=3822 \u7b54\u6848\uff1ax=49 y=41 (40) 28x-62y=-4934 46x+y=552 \u7b54\u6848\uff1ax=12 y=85 (41) 75x+43y=8472 17x-y=1394 \u7b54\u6848\uff1ax=82 y=54 (42) 41x-38y=-1180 29x+y=1450 \u7b54\u6848\uff1ax=50 y=85 (43) 22x-59y=824 63x+y=4725 \u7b54\u6848\uff1ax=75 y=14 (44) 95x-56y=-401 90x+y=1530 \u7b54\u6848\uff1ax=17 y=36 (45) 93x-52y=-852 29x+y=464 \u7b54\u6848\uff1ax=16 y=45 (46) 93x+12y=8823 54x+y=4914 \u7b54\u6848\uff1ax=91 y=30 (47) 21x-63y=84 20x+y=1880 \u7b54\u6848\uff1ax=94 y=30 (48) 48x+93y=9756 38x-y=950 \u7b54\u6848\uff1ax=25 y=92 (49) 99x-67y=4011 75x-y=5475 \u7b54\u6848\uff1ax=73 y=48 (50) 83x+64y=9291 90x-y=3690 \u7b54\u6848\uff1ax=41 y=92 (51) 17x+62y=3216 75x-y=7350 \u7b54\u6848\uff1ax=98 y=25 (52) 77x+67y=2739 14x-y=364 \u7b54\u6848\uff1ax=26 y=11 (53) 20x-68y=-4596 14x-y=924 \u7b54\u6848\uff1ax=66 y=87 (54) 23x+87y=4110 83x-y=5727 \u7b54\u6848\uff1ax=69 y=29 (55) 22x-38y=804 86x+y=6708 \u7b54\u6848\uff1ax=78 y=24 (56) 20x-45y=-3520 56x+y=728 \u7b54\u6848\uff1ax=13 y=84 (57) 46x+37y=7085 61x-y=4636 \u7b54\u6848\uff1ax=76 y=97 (58) 17x+61y=4088 71x+y=5609 \u7b54\u6848\uff1ax=79 y=45 1 2x-10.3x=15 2 0.52x-(1-0.52)x=80 3 x/2+3x/2=7 4 3x+7=32-2x 5 3x+5(138-x)=540 6 3x-7(x-1)=3-2(x+3) 7 18x+3x-3=18-2(2x-1) 8 3(20-y)=6y-4(y-11) 9 -(x/4-1)=5 10 3[4(5y-1)-8]=6 11 10/3 (x/5+3/7)=9x/2 12 5/3\uff08x+0.5)+2=3x-6 13 5x+2(2x/3+2)=2/3(x-6)+2 14 (2x-7)/2-(6x-5)/3=2x+3 15 (3x+2)/5-(x-6)=x/3 16 6x-(x/3+2)=2(x/5+5/2)-3 17 3(x/11-2)-5=2+3x/3 18 10/3(2x-6)=3/5 19 x/2-(x/3-2)=3 20 2/3(x+3)-3=5x/3 21 5/3(2x-5/3)=2x/5-8/9 22 25(x/3-x/2+2/5)-2=3/5(x-2/7)+4/9 23. 15-(8-5x)=7x+(4-3x) 24. 3(x-7)-2[9-4(2-x)]=22 25. 3/2[2/3(1/4x-1)-2]-x=2 26. 2(x-2)+2=x+1 27. 0.4(x-0.2)+1.5=0.7x-0.38 28. 30x-10(10-x)=100 29. 4(x+2)=5(x-2) 30. 120-4(x+5)=25 31. 15x+863-65x=54 32. 12.3(x-2)+1=x-(2x-1) 33. 11x+64-2x=100-9x 34. 14.59+x-25.31=0 35. x-48.32+78.51=80 36. 820-16x=45.5\u00d78 37. (x-6)\u00d77=2x 38. 3x+x=18 39. 0.8+3.2=7.2 40. 12.5-3x=6.5 41. 1.2(x-0.64)=0.54 42. x+12.5=3.5x 43. 8x-22.8=1.2 44. 2(x-2)-3(4x-1)=9(1-x) 45. 11x+64-2x=100-9x 46. (3x+8)/3=41 47. x/4+9x/4=0.25 48. 15x+8-7x=12 49. 48-(x-3)=2+x 50. 3x/6x+4x=9/2 \u5b9e\u6570\u8ba1\u7b97\u9898 1. 3/7 \u00d7 49/9 - 4/3 2. 8/9 \u00d7 15/36 + 1/27 3. 12\u00d7 5/6 \u2013 2/9 \u00d73 4. 8\u00d7 5/4 + 1/4 5. 6\u00f7 3/8 \u2013 3/8 \u00f76 6. 4/7 \u00d7 5/9 + 3/7 \u00d7 5/9 7. 5/2 -\uff08 3/2 + 4/5 \uff09 8. 7/8 + \uff08 1/8 + 1/9 \uff09 9. 9 \u00d7 5/6 + 5/6 10. 3/4 \u00d7 8/9 - 1/3 0.12\u03c7\uff0b1.8\u00d70.9=7.2 (9\uff0d5\u03c7)\u00d70.3=1.02 6.4\u03c7-\u03c7=28+4.4 11. 7 \u00d7 5/49 + 3/14 12. 6 \u00d7\uff08 1/2 + 2/3 \uff09 13. 8 \u00d7 4/5 + 8 \u00d7 11/5 14. 31 \u00d7 5/6 \u2013 5/6 15. 9/7 - \uff08 2/7 \u2013 10/21 \uff09 16. 5/9 \u00d7 18 \u2013 14 \u00d7 2/7 17. 4/5 \u00d7 25/16 + 2/3 \u00d7 3/4 18. 14 \u00d7 8/7 \u2013 5/6 \u00d7 12/15 19. 17/32 \u2013 3/4 \u00d7 9/24 20. 3 \u00d7 2/9 + 1/3 21. 5/7 \u00d7 3/25 + 3/7 22. 3/14 \u00d7\u00d7 2/3 + 1/6 23. 1/5 \u00d7 2/3 + 5/6 24. 9/22 + 1/11 \u00f7 1/2 25. 5/3 \u00d7 11/5 + 4/3 26. 45 \u00d7 2/3 + 1/3 \u00d7 15 27. 7/19 + 12/19 \u00d7 5/6 28. 1/4 + 3/4 \u00f7 2/3 29. 8/7 \u00d7 21/16 + 1/2 30. 101 \u00d7 1/5 \u2013 1/5 \u00d7 21 31.50\uff0b160\u00f740 \uff0858+370\uff09\u00f7\uff0864-45\uff09 32.120-144\u00f718+35 33.347+45\u00d72-4160\u00f752 34\uff0858+37\uff09\u00f7\uff0864-9\u00d75\uff09 35.95\u00f7\uff0864-45\uff09 36.178-145\u00f75\u00d76+42 420+580-64\u00d721\u00f728 37.812-700\u00f7\uff089+31\u00d711\uff09 \uff08136+64\uff09\u00d7\uff0865-345\u00f723\uff09 38.85+14\u00d7\uff0814+208\u00f726\uff09 39.\uff08284+16\uff09\u00d7\uff08512-8208\u00f718\uff09 40.120-36\u00d74\u00f718+35 41.\uff0858+37\uff09\u00f7\uff0864-9\u00d75\uff09 42.(6.8-6.8\u00d70.55)\u00f78.5 43.0.12\u00d7 4.8\u00f70.12\u00d74.8 44.\uff083.2\u00d71.5+2.5\uff09\u00f71.6 \uff082\uff093.2\u00d7\uff081.5+2.5\uff09\u00f71.6 45.6-1.6\u00f74= 5.38+7.85-5.37= 46.7.2\u00f70.8-1.2\u00d75= 6-1.19\u00d73-0.43= 47.6.5\u00d7\uff084.8-1.2\u00d74\uff09= 0.68\u00d71.9+0.32\u00d71.9 48.10.15-10.75\u00d70.4-5.7 49.5.8\u00d7\uff083.87-0.13\uff09+4.2\u00d73.74 50.32.52-\uff086+9.728\u00f73.2\uff09\u00d72.5
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1.下列方程中不一定是一元二次方程的是( )
A.(a-3)x2=8(a≠0) B.ax2+bx+c=0
C.(x+3)(x-2)=x+5 D.
2.已知一元二次方程ax2+c=0(a≠0),若方程有解,则必须有C等于( )
A.- B.-1 C. D.不能确定
3.若关于x的方程ax2+2(a-b)x+(b-a)=0有两个相等的实数根,则a:b等于( )
A.-1或2 B.1或 C.- 或1 D.-2或1
4.若关于y的一元二次方程ky2-4y-3=3y+4有实根,则k的取值范围是( )
A.k>- B.k≥- 且k≠0 C.k≥- D.k> 且k≠0
5.已知方程 的两根分别为a, ,则方程 的根是( )
A. B. C. D.
6.关于x的方程x2+2(k+2)x+k2=0的两个实数根之和大于-4,则k的取值范围是( )
A.k>-1 B.k<0 C.-1<k<0 D.-1≤k<0
7.若方程x2-kx+6=0的两个实数根分别比方程x2+kx+6=0的两个实数根大5,则k的值为( )
A.2 B. C.5 D.-5
8.使分式 的值等于零的x是( )
A.6 B.-1或6 C.-1 D.-6
9.方程x2-4│x│+3=0的解是( )
A.x=±1或x=±3 B.x=1和x=3 C.x=-1或x=-3 D.无实数根
10.如果关于x的方程x2-k2-16=0和x2-3k+12=0有相同的实数根,那么k的值是( )
A.-7 B.-7或4 C.-4 D.4
二、填空题:(每小题3分,共30分)
11.已知3- 是方程x2+mx+7=0的一个根,则m=____________,另一根为____________.
12.已知方程3ax2-bx-1=0和ax2+2bx-5=0,有共同的根-1,则a=____________,b=____________.
13.若一元二次方程ax2+bx+c=0(a≠0)有一个根为1,则a+b+c=____________;若有一个根为-1,则b 与a、c之间的关系为____________;若有一个根为零,则c=____________.
14.若方程2x2-8x+7=0的两根恰好是一个直角三角形两条直角边的长,则这个直角三角形的斜边长是___________.
15.一元二次方程x2-3x-1=0与x2-x+3=0的所有实数根的和等于________________.
16.某食品连续两次涨价10%后价格是a元,那么原价是_____________________.
17.已知两数的积是12,这两数的平方和是25,以这两数为根的一元二次方程是___________.
18.如果关于x的方程x2-2(1-k)+k2=0有实数根α,β,那么α+β的取值范围是_______.
19.设A是方程x2- x-520=0的所有根的绝对值之和,则A2=________.
20.长方形铁片四角各截去一个边长为5cm的正方形,而后折起来做一个没盖的盒子,铁片的长是宽的2倍,作成的盒子容积为1.5 立方分米,则铁片的长等于________,宽等于________.
三、解答题:(每题7分,共21分)
21.设x1,x2是关于x的方程x2-(k+2)x+2k+1=0的两个实数根,且x�0�112+x22=11.
(1)求k的值;(2)利用根与系数的关系求一个一元二次方程,使它的一个根是原方程两个根的和,另一根是原方程两根差的平方.
22.设a、b、c是△ABC的三条边,关于x的方程x2+2 x+2c-a=0有两个相等的实数根,方程3cx+2b=2a的根为0.
(1)求证:△ABC为等边三角形;
(2)若a,b为方程x2+mx-3m=0的两根,求m的值.
23.如图,已知△ABC中,∠ACB=90°,过C点作CD⊥AB,垂足为D,且AD=m,BD= n,AC2:BC2=2:1,又关于x的方程 x2-2(n-1)x+m2-12=0 两实数根的差的平方小于192,求:m,n为整数时,一次函数y=mx+n的解析式.
四、解意自编题:(9分)
24.小李和小张各自加工15个玩具,小李每小时比小张多加工1个,结果比小张少 小时完成任务.问两个每小时各加工多少个玩具?
要求:先根据题意,设合适未知数列出方程或方程组(不需解答),然后根据你所方程或方程组,编制一道行程问题的应用题.使你所列方程或方程组恰好也是你所编的行程应用题的方程或方程组,并解这个行程问题.
五、列方程解应用题:(每小题10分,共20分)
25.国家为了加强对香烟产销的宏观管理,对销售香烟实行征收附加税政策.现在知道某种品牌的香烟每条的市场价格为70元,不加收附加税时,每年产销100万条,若国家征收附加税,每销售100元征税x元(叫做税率x%),则每年的产销量将减少10x万条.要使每年对此项经营所收取附加税金为168万元,并使香烟的产销量得到宏观控制,年产销量不超过50万条,问税率应确定为多少?
26.已知一个小灯泡的额定功率为1.8W,额定电压小于8V.当它与一个30 的电阻并联后接入电路时,干流电路的电流是0.5A,且灯泡正常发光.求小灯泡的额定电压.
参考答案
一、1.B 点拨:ax2+bx+c=0,只有当满足a≠0时,才是一元二次方程.
2.D 点拨:一元二次方程ax2+c=0(a≠0)有解,则ax2=-c,x2= ,因为x2≥0,
∴ ,其解若干,故不能确定.
3.B 点拨:根据一元二次方程的根的判别式,方程有两个相等的实数根,
则△=0,△=[2(a-b)]2-4×a(b-a)=4(a-b)(2a-b),即4(a-b)(2a-b)=0,
∴a=b或a= ,
即a:b=1或a:b=1:2 .
4.B 点拨:由一元二次方程的定义知k≠0,由一元二次方程的根的判别式知方程有实根,
则△≥0,即k≥ ,故k≥ 且k≠0,本题易漏k≠0和△=0两个条件.
5.D 点拨:由 ,得 ,可变为 ,所以其解为x-1=a-1,即x=a或x-1= ,即x= .此题易误解为x=a或x= .
6.D. 点拨:方程有两个实数根,所以△≥0,即[2(k+2)]2-4k2≥0,解得k≥-1,两实数根之和大于-4,即-2(k+2)>-4,k<0,
∴-1≤k<0.本题易忽略有两实根,需满足△≥0这个重要条件.
7.D.点拨:设x2-kx+b=0的两根为x1,x2,则x2+kx+6=0的两根为x1+5,x2+5,因为x1+x2=k,(x1+5)+(x2+5)=-k所以k=-5.
8.A 点拨:使分式的值为零的条件:分子=0分母≠0,x2-5x-6=0,x=6或-1,x+ 1≠0,x≠-1,故x=6,本题易漏分母不能为零这个条件.
9.A 点拨:∵x2≥0,│x│≥0,∴x2-4│x│+3=0的解就是方程│x│2-4│x│+3=0的解,(│x│-3)(│x│-1)=0,x=±3或x=±1.
10.D 点拨:两方程有相同实根,则x2+k2-16=x2-3k+12,解得k=-7或4,
当k=- 7时,方程无实根,∴k=4.
二、
11.m=-6,另一根为3+ .
点拨:根据一元二次方程根与系数的关系,设方程另一个根为x1 ,
则(3- )x1=7,x1=3+ ,(3+ )+(3- )=-m,则m=-6.
12.a=1,b=-2.点拨:-1是两方程的根,则3a+b-1=0,a-2b-5=0,解得a=1,b=-2.
13.a+b+c=0,b=a+c,c=0.
14.3 点拨:设两根为x1,x2,根据根与系数的关系x1+x2=4,x1�6�1x2= ,
由勾股定理斜边长的平方=(x1+x2)2-2x1x2=16-2× =9,∴斜边长为3.
15.3 点拨:x2-3x-1=0的△=13>0,x2-x+3=0的△=-11<0所有实根和,就是方程x2-3x-1=0中两根之和,由根与系数的关系求得两根之和等于3.
16. 元 点拨:设原价x元,则x(1+10%)2=a,解得x= .
17.x2+7x+12=0或x2-7x+12=0 点拨:设两数为a,b,则ab=12,a2+b2=25,
∴( a+b)2-2ab=25,(a+b)2=49,(a+b)=±7,
所以以a,b为根的方程为x2+7x+12= 0 或x2-7x+12=0.
18.a+β≥1 点拨:方程有实根,则△≥0,则k≤ ,即-k≥- ,1-k≥1- ,2(1-k)≥1,∵a+β=2(1-k),∴a+β≥1.
19.4083 点拨:由公式法得x= ,则
=
∴A2=4083
20.60,30 解:设宽为xcm,则长为2xcm,由题意得(2x-10)×(x-10)×5=1500,
解得x1=20,x2=-5(舍去),2x=40. 本题注意单位要一致.
三、
21.k=-3,y2-20y-21=0
解:(1)由题意得x1+x2=k+2,x1�6�1x2=2k+1,x12+x22=(x1+x2)2-2 x1�6�1x2=k2+2,又x12+x22=11,
∴k2+2=11,k=±3,
当k=3时,△=-3<0,原方程无实数解;当k=-3时,△=21>0,原方程有实数解,故k=-3.
(2)当k=-3时,原方程为x2+x-5=0,设所求方程为y2+py+q=0,两根为y1,y2,
则y1=x1+x2=-1,y2=(x1-x2)2=x12+x22-2x1x2=11+10=21,
∴y1+y2=20,y1y2=-21,故所求方程是y2-20y-21=0.
点拨:要求k的值,须利用根与系数的关系及条件x12+x22=(x1+x2)2-2 x1�6�1x2,构造关于k的方程,同时,要注意所求出的k值,应使方程有两个实数根,即先求后检.
(2)构造方程时,要利用p=-(y1+y2),q=y1y2,则以y1,y2为根的一元二次方程为y2+py+q=0.
22.(1)证明:方程x2+2 x+2c-a=0有两个相等的实根,
∴△=0,即△=(2 )2-4×(2c-a)=0,
解得a+b=2c,方程3cx+2b=2a的根为0,则2b=2a,a=b,
∴2a=2c,a=c,
∴a=b=c,故△ABC为等边三角形.
(2)解:∵a、b相等,∴x2+mx-3m=0有两个相等的实根,
∴△=0,∴△=m2+4×1×3m=0,
即m1=0,m2=-12.
∵a、b为正数,
∴m1=0(舍),故m=-12.
23.解:如答图,易证△ABC∽△ADC,
∴ ,AC2=AD�6�1AB.同理BC2=BD×AB,
∴ ,
∵ ,
∴ ,∴m=2n ①.
∵关于x的方程 x2-2(n-1)x+m2-12=0有两实数根,
∴△=[-2(n-1)2-4× ×(m2-12)≥0,
∴4n2-m2-8n+16≥0,
把①代入上式得n≤2 ②.
设关于x的方程 x2-2(n-1)x+m2-12=0的两个实数根分别为x1,x2,
则x1+x2=8(n-1),x1�6�1x2=4(m2-2),
依题意有(x1-x2)2<192,即[8(n-1)]2-4(m2-12)]<192,
∴4n2—m2-8n+4<0,把①式代入上式得n> ③,由②、③得 <n≤2,
∵m、n为整数,∴n的整数值为1,2,
当n=1,m=2时,所求解析式为y=2x+1,当n=2,m=4时,解析式为y=4x+2.
四、
24.解:设小张每小时加工x个零件,则小李每小时加工x+1个,
根据题意得 ,解得 x1=-6(舍),x2=5.
所以小张每小时加工5个零件,只要符合条件就行,本题是开放性题目,答案不惟一.
五、
25.解:根据题意得70(100-10x).x%=168,x2-10x+24=0,解得 x1=6,x2=4,
当x2=4时,100-10×4=60>50,不符合题意,舍去,x1=6时,100-10×6=40<50,
∴税率应确定为6%.
点拨:这是有关现实生活知识应用题,是近几年中考题的重要类型,要切实理解,掌握.
26.解:设小灯炮的额定电压为U,根据题意得:
, ,解得U1=6,U2=9(舍去)
∵额定电压小于8V,∴U=6.
答:小灯泡的额定电压是6V.
点拨:这是一道物理与数学学科间的综合题目,解答此问题的关键是熟记物理公式并会解可化为一元二次方程的分式方程,检验是本题的易忽略点.已知x平方-5xy-6y平方=0,且xy不等于0,则y分之x的值为( )
A、6 B、-1 C、1或-6 D、-1或6
x�0�5-5xy-6y�0�5=0
这题可以用十字相乘法
1 1
1 -6
-6+1=-5,刚好等于xy的系数。
所以这个方程可化为(x+y)(x-6y)=0
所以x+y=0 或 x-6y=0
x=-y x=6y
所以x/y=-y/y=-1 或 x/y=6y/y=6
故选D。
1)36x^2-1=0 36x的平方-1=0
(2)4x^2=81 4x的平方=81
(3)(x+5)^2=25 (x+5)等平方=25
(4)x^2+2x+1=4 x的平方+2x+1=4
1)36x^2-1=0
(6x+1)(6x-1)=0
6x+1=0
6x-1=0
x1=-1/6
x2=1/6
(2)4x^2=81
4x^2-81=0
(2x+9)(2x-9)=0
2x+9=0
2x-9=0
x1=9/2
x2=-9/2
(3)(x+5)^2=25
x+5=5
x+5=-5
x1=0
x2=-10
(4)x^2+2x+1=4
(x+1)^2=4
x+1=2
x+1=-2
x1=1
x2=-3
这也太多了吧,50道
去网上找一下啊
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